Power for PPI++ two-sample t-test (difference in means)

Computes power for a two-sample t-test using PPI++ where we estimate the difference in means between two independent groups.

Usage

power_ppi_ttest(
  delta,
  n_A,
  n_B,
  N_A,
  N_B,
  alpha = 0.05,
  sigma_y2_A,
  sigma_f2_A,
  cov_yf_A,
  sigma_y2_B,
  sigma_f2_B,
  cov_yf_B
)

Arguments

delta

Effect size: the true difference in means \(\mu_A - \mu_B\).

n_A

Labeled sample size for group A.

n_B

Labeled sample size for group B.

N_A

Unlabeled sample size for group A.

N_B

Unlabeled sample size for group B.

alpha

Two-sided significance level (default 0.05).

sigma_y2_A

Variance of outcomes in group A.

sigma_f2_A

Variance of predictions in group A.

cov_yf_A

Covariance between Y and f in group A.

sigma_y2_B

Variance of outcomes in group B.

sigma_f2_B

Variance of predictions in group B.

cov_yf_B

Covariance between Y and f in group B.

Value

Scalar power in \([0, 1]\).

Details

The variance of the difference estimator is the sum of the PPI++ variances from each group (assuming independence): $$\mathrm{Var}(\hat\mu_A - \hat\mu_B) = \mathrm{Var}_{PPI++}(\hat\mu_A) + \mathrm{Var}_{PPI++}(\hat\mu_B)$$

Examples

# Two-sample test with equal groups
power_ppi_ttest(
  delta = 0.3,
  n_A = 100, n_B = 100,
  N_A = 5000, N_B = 5000,
  sigma_y2_A = 1, sigma_f2_A = 1, cov_yf_A = 0.7,
  sigma_y2_B = 1, sigma_f2_B = 1, cov_yf_B = 0.7
)
#> [1] 0.8371692